The exponential growth of data generated at the network edge has driven a paradigm shift from centralized cloud computing to local edge processing, accelerating the widespread adoption of edge computing across diverse applications. In this context, continual test-time adaptation (CTTA) on edge devices, which enables models to adapt to evolving target domains without access to source data or labeled samples, has become an emerging research focus due to its practical importance in dynamic environments with changing data distributions. However, limited computational and memory resources severely restrict CTTA on edge devices. Moreover, since adaptation relies on noisy unsupervised losses without access to labels, prolonged CTTA can lead to error accumulation. Additionally, the model is susceptible to catastrophic forgetting, an intrinsic challenge in continual adaptation. In this paper, we propose MccTTA, a memory efficient collaborative continual test-time adaptation framework for edge devices. Specifically, MccTTA incorporates a generative model to synthesize images as a replacement for replay data on the cloud, and a lightweight side network attached to the frozen original network to reduce memory consumption during edge adaptation. We further introduce 2SR (Two-Stage Rehearsal), which decouples active forgetting and knowledge integration into two separate stages to address the plasticity–stability dilemma caused by distributional discrepancies between synthetic and real task data during continual adaptation. Finally, extensive experiments are conducted to evaluate the effectiveness of MccTTA. The results show that, compared with conventional TTA methods, MccTTA achieves superior accuracy and mitigates forgetting while requiring less memory.